Asked by monic
Differentiate.
f(x) = 8 − x^ex/x + ex
f '(x) =
f(x) = 8 − x^ex/x + ex
f '(x) =
Answers
Answered by
Steve
Hard to tell just what you mean there. If you mean
f(x) = (8-xe^x)/(x+e^x)
f' = [(-e^x - xe^x)(x+e^x) - (8-xe^x)(1+e^x)]/(x+e^x)^2
= (-xe^x - x^2 e^x - e^2x - xe^2x - 8 + xe^x - 8e^x + xe^2x)/(x+e^x)^2
= (e^x(-x+x^2-e^x-xe^x+x-8+xe^x)-8)/(x+e^x)^2
= (e^x(x^2-e^x-8)-8)/(x+e^x)^2
doesn't get much simpler
If I got the original wrong, fix it and visit wolframalpha.com
f(x) = (8-xe^x)/(x+e^x)
f' = [(-e^x - xe^x)(x+e^x) - (8-xe^x)(1+e^x)]/(x+e^x)^2
= (-xe^x - x^2 e^x - e^2x - xe^2x - 8 + xe^x - 8e^x + xe^2x)/(x+e^x)^2
= (e^x(-x+x^2-e^x-xe^x+x-8+xe^x)-8)/(x+e^x)^2
= (e^x(x^2-e^x-8)-8)/(x+e^x)^2
doesn't get much simpler
If I got the original wrong, fix it and visit wolframalpha.com
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.